Can x/0 be divided out

1. Apr 2, 2004

ShawnD

Say I had an expression that went like this

$$\frac{ 5 \frac{x}{0} }{3 \frac{x}{0} }$$

Can I divide those $\frac{x}{0}$ terms or do they make the expression undefined?

2. Apr 2, 2004

chroot

Staff Emeritus
Nope, you can't divide them out. The entire expression is indeterminate (NOT undefined).

- Warren

3. Apr 2, 2004

matt grime

I wouldn't say you can't divide them out so much as what you wrote is just plain wrong, being polite about it - the symbols make no sense as written.

4. Apr 2, 2004

chroot

Staff Emeritus
I think he means

$$\frac{ 5 \cdot \frac{x}{0} }{3 \cdot \frac{x}{0} }$$

to be read "5 times x over 0...", not "5 and x zeroths..."

- Warren

5. Apr 3, 2004

matt grime

But is still makes no sense. x/0 is not a well-defined symbol in the real number system that one can manipulate like this.

6. Apr 3, 2004

Chen

I think that was part of his question.

7. Apr 3, 2004

Organic

1/0.1 is tha same as 1*10
1/0.01 is tha same as 1*100
1/0.001 is tha same as 1*1000
and so on ...

1/0 is the same as 1*oo and in both cases we are no longer in a finite system.

oo is a general notation for infinity therefore 1/0 is also a general notation for infinity.

8. Apr 3, 2004

Zurtex

Note for others, in the link given it goes points out:

"Informally,[itex]1 / \infty = 0[/tex] , a statement which can be made rigorous using the limit concept"

You can't just say:

$$\frac{1}{\infty} = 0$$

or any manipulation of that as and think it is mathematically true.

9. Apr 4, 2004

Hurkyl

Staff Emeritus